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III.—The Simplest Form of Second-Order Linear Differential Equation, with Periodic Coefficient, having Finite Singularities*

Published online by Cambridge University Press:  14 February 2012

Enzo Cambi
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Synopsis

A differential equation of the second order, arising in problems of disturbed oscillation, such as occur in frequency modulation, is considered. The nature of its solutions is examined by the method of continued fractions. The cases in which the solutions are periodic, and the regions of stability and instability (lability), are determined according to the values taken by the two parameters involved.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 63 , Issue 1 , 1950 , pp. 27 - 51
Copyright
Copyright © Royal Society of Edinburgh 1950

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References

References to Literature

Nörlund, N. E., 1924. Vorlesungen über Differenzenrechnung, Berlin.CrossRefGoogle Scholar
Sansone, G., 1941. Le equazioni differenziali nel campo reale, Bologna. Esp. Chapter VI.Google Scholar
Strutt, M. J. O., 1932. Lamé-sche, Mathieu-sche, und verwandte Funktionen, Berlin. This contains an extensive bibliography on Hill's problem.Google Scholar
Strutt, M. J. O., 1943. Eigenwaarde-Krommen bij Problemen van Hill, I and II, Amsterdam.Google Scholar
Strutt, M. J. O., 1943. Eigenfuncties bij Problemen van Hill, I and II, Amsterdam.Google Scholar
Tannery, J., and Molk, J., 1898. Fonctions Elliptiques, Paris.Google Scholar
Whittaker, E. T., and Watson, G. N., 1927. Modern Analysis, Cambridge. Esp. Chapter XIX.Google Scholar